A square is inscribed in a circle. Write the area of the square as a function of the radius.

Answer:

27.3

Step-by-step explanation:

21 times 1.3 = 27.3 = original price

She paid 70% of the regular price of $30.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Eliza bought a hat for $21. The regular price is $30. The percentage will be calculated as,

Percentage = 21 / 30

Percentage = 0.7 x 100

Percentage = 70%

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The required angles  ∠TBS and ∠TCV are 48° and 22° respectively.

A right-angled triangle is a kind of triangle that has one of its points equivalent to 90 degrees. The other two points summarize to 90 degrees. The sides that incorporate the right point are opposite and the foundation of the triangle. The third side is known as the hypotenuse, which is the longest side of each of the three sides

∠TBV = 24°

∠VBS = 24°

So, ∠TBS = (24° ) = 48°

And,

∠SAU = 92°,

So,

∠VAU = 46°

In ΔTAC

∠TAC + ∠TCA = 90°

∠TCA = 90° - 46° = 44°

This angle is bisect by CV

Then,

∠TCV = 44/2 = 22°

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∠TBS = 48°

SV = 17

∠TCV = 20°

What is a angle bisector?

In geometry, an angle bisector is a line that divides an angle into two equal angles. The term "bisector" refers to a device that divides an object or a shape into two equal halves. An angle bisector is a ray that divides an angle into two identical segments of the same length.

As given in question:

AV , BV and CV are the angle bisector of ΔABC

UV = 17, BV = 18

∠SAU =92° and ∠TBV = 24°

Now,

∠TBV = ∠SBV = 24° ( BV is angle bisector)

So, ∠TBS = ∠TBV + ∠SBV

      ∠TBS = 24° + 24° = 48°

SV = UV = 17 (V is the incenter of ΔABC.)

∠SAU + ∠TBS + ∠TCU = 180° (Sum of angles of a triangle)

92° + 48° + ∠TCU = 180°

∠TCU = 180° - 140°

∠TCU = 40°

So, [tex]\angle TCV = \frac{40\degree}{2}[/tex]

       ∠TCV = 20°

∴ ∠TBS = 48°

SV = 17

∠TCV = 20°

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Answer:

-4

Step-by-step explanation:

Take two points and plug into the distance formula  [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]

We will use (-2, 17) for ([tex]x_{1} , y_{1}[/tex]) and (-1, 13) for ([tex]x_{2} , y_{2}[/tex])

[tex]\frac{13- 17}{-1- -2}[/tex] = [tex]\frac{-4}{1} = -4[/tex]

Answer: I believe 140

Step-by-step explanation: This is how I found my answer:

420 / 3

= 140

420-140

=  280

420= number of all tickets sold.

140= number of adult tickets sold

280= number of student tickets sold

You might wonder how I know why it's 140. I know it's 140, because using my context clues, it stated:

"the number of student tickets sold was three times the number of adult tickets."

So, the one that was the bigger amount must be the student's tickets sold, while the lower amount has to be the adult's tickets sold. I hope this helped!

The value of measure of ''angle f'' in the figure will be 46°.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

In the figure,

The value of angle a and e are;

⇒ a = 115°

⇒ e = 69°

Now,

Since, There are two parallel lines shown in figure.

Hence, We know by the definition of alternate angles of parallel lines,

⇒ ∠a = ∠f + ∠e

Here, We have to given that;

The angles are,

⇒ a = 115°

⇒ e = 69°

So, We get by substitute the value of angle a and e;

⇒ ∠a = ∠f + ∠e

⇒ 115° = ∠f + 69°

Subtract 69° both side, we get;

⇒ ∠f = 115° - 69°

⇒ ∠f = 46°

Thus, The value of measure of angle f;

⇒ ∠f = 46°

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Answer:

m angle B = 27.54 degree

m angle C = 60.85 degree

Step-by-step explanation:

angle A is 90º so the other two angles must sum to 90º

2x+5x-8=90

7x-6=90

7x=96

x=13.77

therefore,

m angle B = 27.54 degree

m angle C = 60.85 degree

The cartesian coordinates of the given polar coordinates are

(A) (2, π); (X, Y) = (-2, 0)

(B) (6, -2π/3); (X, Y) = (-3, -3√3)

The cartesian coordinates for the polar coordinates are calculated by the formulae,

x = rcosθ, and y = rsinθ

Where the polar coordinates are (r, θ).

The cartesian coordinates for the given polar coordinates are as follows:

(A) (r, θ) = (2, π)

Then,

x = r cosθ = 2 cos(π) = 2(-1) = -2

y =r sinθ = 2 sin(π) = 2(0) = 0

Therefore, the cartesian coordiantes are (X, Y) = (-2, 0).

(B) (r, θ) = (6, -2π/3)

Then,

x = r cosθ = 6 cos(-2π/3) = 6(-1/2) = -3

y =r sinθ = 6 sin(-2π/3) = 6(-√3/2) = -3√3

Therefore, the cartesian coordinates are (X, Y) = (-3, -3√3)

The plot for the given polar coordinates on a polar grid is shown below:

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Answer: The common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.

Step-by-step explanation: The common ratio r of a geometric sequence is found by dividing the second term by the first term, and the nth term of the geometric sequence is given by a1 * r^(n-1), where a1 is the first term.

To find the common ratio r of this geometric sequence, we can use the fact that the 3rd term is -18 and the 6th term is 9216:

-18 = a1 * r^2

9216 = a1 * r^5

Dividing these two equations, we get:

-18/9216 = (a1 * r^2) / (a1 * r^5)

-18/9216 = r^-3

r = (-18/9216)^(-1/3)

Since r is the common ratio, it must be positive. Since (-18/9216)^(-1/3) is negative, we must take the positive root:

r = ((-18/9216)^(-1/3))^(1/3)

r = ((-18/9216)^(1/9))

r = (9216/-18)^(1/9)

r = (-512)^(1/9)

r = (-8)^(1/9)

r = (-2)^(2/9)

r = (-2)^(2/3)

r = (1/4)^(2/3)

r = 1/2

To find the first term a1, we can use the fact that the 3rd term is -18 and the common ratio is 1/2:

-18 = a1 * (1/2)^2

-18 = a1/4

a1 = -72

To find the 4th term a4, we can use the fact that the first term is -72 and the common ratio is 1/2:

a4 = (-72) * (1/2)^3

a4 = -9

Therefore, the common ratio of the geometric sequence is 1/2, the first term is -72, and the 4th term is -9.

The 1 dollars found near the table by your friend is likely the money for the tickets.

You are selling tickets at a dance. Individual tickets cost $6, and 2 tickets for a couple cost $10. After the dance, you count $1075 and 195 tickets.

let

x = number of individual ticket

y = number of couple tickets = 2x

Therefore, using equation,

2x(10) + 6x = 1075

2x + x = 195

Hence,

20x + 6x  = 1075

3x = 195

x = 195 / 3

x = 65

Hence,

26x = 1075

26(65) = 1690

Therefore, the money on the table is the ticket money because the money is short of the amount of the tickets in dollars.

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Answer:

Bro you require a protector to measure angle

Answer:

A. 45 degrees

B.90 degrees

Step-by-step explanation:

For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.

The state of not being equal, particularly in terms of status, rights, and opportunities, is a fundamental concept in social justice theories. It can be perplexing in public conversation since it typically has distinct meanings to different individuals. However, some variations are common. An inequality in mathematics is a comparison between two numbers or other mathematical expressions that is unfair. Various notations are used to denote different kinds of inequality, including:

A less than sign, such as a, denotes that an is greater than b.

Given inequality is:

|2x+7|+9 >18.

First we have to rearrange all the variables to the left side of the given equation:

Then,

|2x+7|>18-9

|2x+7|>9

2x+7>9 or 2x+7< -9

S0, x>1 or x< -8

Therefore, x< -8 or x>1

Hence, For the given inequality of |2x+7|+9 >18 the values of x are x< -8 or x>1.

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The equivalent expression by combining like terms is 1.10b and

If the cost increases by 10%, you can multiply the former cost by 110%

From the question, we have the following parameters that can be used in our computation:

Expression of 10% raise = b + 0.10b

Evaluate the like terms in the above expression

So, we have the following representation

Expression of 10% raise = 1.10b

Hence, the expression is 1.10b

Recall that we have the mathematical statement to be

If the cost increases by 10%, you can multiply the former cost by %.

In this case, the factor is calculated as

factor = 1 + 10%

So, we have

Factor = 110%

So, the missing expression in the statement 110%

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Therefore the solution of this question is  the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

Here,

The perimeter of the square drawn on the grid

The vertices given in the question are (3,3) & (7,7)

The length of the vertices given=[tex]\sqrt{(x_{2} -x_{1})^{2} +(y_{2}- y_{1})^{2} }[/tex]

Thus at vertices  (3,3) & (7,7)

=>[tex]\sqrt{(7 -3)^{2} +(7-3)^{2} }[/tex]

=>4[tex]\sqrt{2}[/tex]

Therefore the perimeter of the square = 4a

thus,

=>4*4[tex]\sqrt{2}[/tex]

=>16[tex]\sqrt{2}[/tex] units

Therefore the perimeter of the square on the grid is 16[tex]\sqrt{2}[/tex] units

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Answer:

83

Step-by-step explanation:

(78+72+87+90+x)/5=82

327+x=82*5

327+x=410

x=410-327

x=83

Answer:

Below

Step-by-step explanation:

k = 4-a

a (4-a) = 3

-a^2 +4a -3 = 0   ====> Quadratic Formula ===>  a =  1   and k = 3

1^3 + 3^3 = 28

Twice a day for 20 minutes is the required time to realize that meditation practiced is beneficial for persons physical and mental health.

Meditation practiced helps person in different ways:

Twice a week is very less time and does not make consistency.

Incorrect option.

Several hours at a stretch is not possible for all individual and it is not practical .

Incorrect option.

Twice a day for 20 minutes is the best time and helps individual to practice  meditation.

Therefore, Option C. twice a day for 20 minutes is the best time for mediation.

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The given statement " in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables. " is false.

In math chi square test means the process of determine if there is a significant relationship between two nominal (categorical) variables.

Here we have the statement, in the chi-square test of independence, large values of the chi-square test statistic indicate a cause/effect relationship between the two categorical variables.

And we need to find the statement is true or not.

According to the definition of chi square test, we know that it checks whether two variables are likely to be related or not.

Here we have counts for two categorical or nominal variables.

So, there is no large value comparision take palce.

Therefore, the statement is false.

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Probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.

Convenience sampling is any non sampling technique where units are chosen for the sample based on their accessibility to the researcher.

Thus, probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.

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1. The slope of Abha's climb is 2 (rise/run).

2. No, the line 54y=13x does not pass through the origin.

3. The y-intercept of the line is 5.

4. The equation of the line is y = -5x + 3.

A linear function is one that has one or two variables and no exponents, according to the definition given in mathematics. It is a graphing function that produces a straight line.

To finish the graph, use a straightedge to draw a line through the two points as two points decide a line. The formula for a linear function is f(x)=mx+b, where m and b are real values representing the slope. Set f(x)=0 and work out the value of x to determine the x-intercept, if one exists. We can use y and f(x) interchangeably because y=f(x).

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Answer: 12.5%

Step-by-step explanation:

Take 1750 divided by 1999, then time 100% = 87.5%

100% - 87.5% = 12.5%

The rate of discount is 12.5%

Answer:

Window view rooms is 50, no window view rooms is 150.

Step-by-step explanation:

I just multiplied the prices times random number of rooms until they added together to 8,500$. It was purely by chance that I discovered the answer ngl to you lol

In linear equation,   20x + 45y = 440 ,     y = 2x  Where x is the number of small boxes sent and y  is the number of large boxes sent.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Let be x the number of small boxes sent and y the number of large boxes sent.

Since each small box can hold 20 books (20x), each large box can hold 45 books (45y)and altogether can hold a total of 440 books, we can write the following equation to represent this

                 20x + 45y = 440

According to the information provided in the exercise, there were 4 times as many large boxes sent as small boxes. This can be represented with this equation

              y = 2x

Therefore, the system of equation that be used to determine the number of small boxes sent and the number of large boxes sent, is

                20x + 45y = 440

                      y = 2x

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The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.

Given that, f(x)=x²+2x-4 and g(x) =[tex]\frac{1}{(x+1)}[/tex].

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, (g·f)(x) can be determined as follows

(g·f)(x)=g(x)×f(x)

= [tex]\frac{1}{(x+1)} \times x^2+2x-4[/tex]

Find the domain by finding where the expression is defined.

Interval Notation:

(-∞,-1)∪(-1,∞)

Set-Builder Notation:

{x∈ℝ|x ≠ -1}

The domain of the function (g·f)(x) is {x∈ℝ|x ≠ -1}. Therefore, option B is the correct answer.

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The inequality that is used to find the domain of the function would be B x - 3 ≥ 0

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The given function is f(x) = √x - 3

Here we have to find the inequality that is used to find the domain of the function.

Therefore, the function (x - 3) must be greater than or equal to 0

That is;

x - 3 ≥ 0

We will use the above inequality to find the domain of the function.

When we solve the above inequality, we get the domain of the function then;

x - 3≥0

Now add 3 on both sides, we get;

x - 3 + 3 ≥ 0 + 3

x ≥ 3

Therefore,  the answer is x - 3 ≥ 0

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The real and complex solutions of the polynomial equation [tex]x^{3} - 8[/tex] = 0 is 2,  -1 + [tex]\sqrt{3}[/tex]i  and  -1 - [tex]\sqrt{3}[/tex]i. option 2 is correct.

Polynomial equations are those created using exponents, coefficients, and variables. The greater of its possible exponents is referred to as the equation's degree. By factoring polynomials according to their degree and the variables in the equation, we may find their solutions.

Our equation is [tex]x^{3} - 8[/tex]

and we know that:  [tex]x^{3} = 8[/tex]

then we can write our equation as: [tex]x^{3} - 2^{3}[/tex]

And using the identity: [tex]a^{3} - b^{3} = (a-b) *(a^{2} +ab+b^{2} )[/tex]

where a = x and b = 2, then our equation is:

them, if x = 2 the first part is zero, so x = 2 is a solution, and now we need to see the second part in order to find the complex solutions.

[tex]x^{2} + 2x +2^{2}[/tex] = 0

Here we need to use.

a[tex]x^{2}[/tex] + bx + c = 0 if  for a, b and c constants, then:

x = [tex]-b +-\sqrt{b^{2} - 4ac } /2a[/tex]

in our problem we have:

x = -2 +-[tex]\sqrt{4 - 16}[/tex] /2

x = -1 +-[tex]\sqrt{-3}[/tex]

x =  -1 +-[tex]\sqrt{3}[/tex] i

So here we have two complex solutions:  -1 + [tex]\sqrt{3}[/tex]i  and  -1 - [tex]\sqrt{3}[/tex]i

So the value of x are 2,  -1 + [tex]\sqrt{3}[/tex]i  and  -1 - [tex]\sqrt{3}[/tex]i

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I think you mean

What are the real and complex solutions of the polynomial equation? (1 point)

[tex]x^{3} - 8[/tex] = 0

( the equation is [tex]x^{3} - 8[/tex] = 0 and not x-8 =0)

Part a: Time taken to double the population of chipmunks is 5/2 months.

Part b: Population at population size; P = 200 is 50.

Part a: Time taken to double the population of chipmunks;

P(t) = 100[1 + (0.3)t + (0.04)t²].

P(0) = 100[1 + 0 + 0] = 100

P(t) = 200 = 100 + 30t + 4t²

4t² + 30t − 100 = 0

2t² + 15t − 50 = 0

(2t − 5)(t + 10) = 0

t = 5/2

It will take 5/2 months population to double its initial size P(0).

Part b: Population at population size; P=200

P'(t) = 0 + 30 + 8t

P = 200 when t = 5/2

P'(200) = 30 + 8(5/2)

P'(200) = 30 + 20

P'(200) = 50

Thus, the instantaneous rate of growth of the population when the population size is P=200 is 50.

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In the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

So, in this instance, the multiplication is as follows:

5 * 216

This multiplication can be rewritten as follows:

5*(200+16)

We then put the distributive property to use. So, we have:

(5*200) + (5*16)

Therefore, in the given situation where Jack writes 5 * 216 as (5*200) + (5*16), he uses the distributive property.

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Correct question:
Jack broke apart 5x216 as (5x200)+(5x16) to multiply mentally. What strategy did Jack use?

Answer:

-1.8x^2

Step-by-step explanation: